2.78 broke all of my files' texture rendering
The real issue is that the subdivision surface modifier on the main plane is set to a different value between preview and render:



Additionally, the way Dupvertex interprets object scaling has been changed in 2.79. The best way to move forward is to scale the 'pixel' cube into a square and then apply the scale with Ctrl+A:



Finally, adjust the bevel modifier to get the right amount of bevel again.